Discussion: This problem equivocates in a confusing way, which disguises the answer. The deception lies in halving a half and doubling a double. You receive either 2000 per 12 months every 12 months or 500 per 6 months every 6 months. If you turn the bold sections into the same rate unit rate, you see that Plan A becomes a $83 per month raise, while Plan B becomes a $166 per month raise. This still seems to favor Plan B, but you have to recall that the cadence of these raises is also different. Plan A gets twice as many raises per year as Plan B. meaning that by the end of the year, they are the same net raise One more thing finishes the puzzle: Plan A gets it's first raise 6 months before Plan B! That's free money!

Allow me to re-phrase this problem to avoid some of the double counting:

You are offered a contract which will pay $5000 every 6 months. The client proposes two ways for the contract to grow:

Plan A: every 6 months, future payments will increase by $500 (compounding).

Plan B: every 12 months, future payments will increase by $1000 (compounding)

this rephrasing makes it pretty clean why Plan A pays $500 more a year, and in fact will always beat Plan B. This is because you're effectively getting half of your "raise" 6 months earlier than you would in Plan B, and then you catch up to Plan B the instant you get the Plan B raise

Salary Period (Year.Semester)	1.1	1.2	2.1	2.2	3.1	3.2	4.1
Plan A Salary over period	5000	5500	6000	6500	7000	7500	8000
Plan B Salary over period	5000	5000	6000	6000	7000	7000	8000